Linear Algebra

Author: Wang Wen-sheng
Publisher:
Publish Date: 2004-05-01
Features: This textbook is based on the author's many years of using lecture notes and primarily reflects the following features:
1. Emphasizes the connection between theory and practice, introducing concepts and theorems as much as possible from practical and real-world problems. It highlights the close relationship between higher algebra and modern technology and social life, emphasizing its applications in modern technology.
2. Focuses on the connection between higher algebra and elementary mathematics to cultivate students' ability to solve elementary mathematical problems from a broader perspective. This connection is primarily reflected in some examples and exercises.
3. Emphasizes the humanistic spirit. The textbook includes brief biographies of mathematicians—Spotlight on Figures—to help students understand the outstanding contributions of mathematicians to the history of mathematics.
4. Focuses on fostering an innovative spirit. The textbook includes "Exploring Problems" for students interested in exploring new approaches and innovative solutions.
5. Strengthens the teaching of fundamental concepts, paying attention to introducing the process of how basic concepts and principles are developed. It emphasizes cultivating students' abilities to observe, think, ask questions, and solve problems.
6. The textbook is equipped with typical examples, avoiding the isolation of solving various special cases. Instead, it focuses on analyzing ideas and broadening thinking, seeking general patterns and methods for a class of problems to achieve broader application.
7. Exercises are arranged by section, with varying levels of difficulty, and a large number of supplementary problems are provided at the end of each chapter.
8. To meet the needs of bilingual teaching and enhance students' professional English skills, important keywords are annotated with their English equivalents. The book consists of ten chapters. The first three chapters cover determinants, systems of linear equations, and matrices. Chapter 4 is on polynomial theory, which uses n-dimensional vectors and their linear relationships to comprehensively solve the theory of linear equations. It also studies the operational properties of matrices and related rank problems using n-dimensional vector theory. Additionally, it uses n-dimensional vectors and matrices to represent polynomial operations, operational properties, and greatest common divisors, fully demonstrating the application of matrix theory in polynomials, which is a key difference from other textbooks. The last six chapters cover quadratic forms, linear spaces, linear transformations, Euclidean spaces, and bilinear functions.